1. Field of the Invention
The present invention relates to imaging devices such as cameras, video cameras, microscopes, and other visualization techniques, and more particularly, to the acquisition of images and video using fewer measurements than previous techniques.
2. Brief Description of the Related Art
The large amount of raw data acquired in a conventional digital image or video often necessitates immediate compression in order to store or transmit that data. This compression typically exploits a priori knowledge, such as the fact that an N-pixel image can be well approximated as a sparse linear combination of K<<N wavelets. These appropriate wavelet coefficients can be efficiently computed from the N pixel values and then easily stored or transmitted along with their locations. Similar procedures are applied to videos containing F frames of P pixels each; where N=FP denotes the number of video “voxels”.
This process has two major shortcomings. First, acquiring large amounts of raw image or video data (large N) can be expensive, particularly at wavelengths where CMOS or CCD sensing technology is limited. Second, compressing raw data can be computationally demanding, particularly in the case of video. While there may appear to be no way around this procedure of “sample, process, keep the important information, and throw away the rest,” a new theory known as Compressive Sensing (CS) has emerged that allows for directly acquiring a compressed digital representation of a signal without first sampling that signal. See Candes, E., Romberg, J., Tao, T., “Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inform. Theory 52 (2006) 489-509; David Donoho, “Compressed sensing,” IEEE Transactions on Information Theory, Volume 52, Issue 4, April 2006, Pages: 1289-1306; and Candes, E., Tao, T., “Near optimal signal recovery from random projections and universal encoding strategies,” (2004) Preprint.
Efforts on compressed imaging include Pitsianis, N. P., Brady, D. J., Sun, X.: “Sensor-layer image compression based on the quantized cosine transform,” SPIE Visual Information Processing XIV (2005) and Brady, D. J., Feldman, M., Pitsianis, N., Guo, J. P., Portnoy, A., Fiddy, M., “Compressive optical MONTAGE photography,” SPIE Photonic Devices and Algorithms for Computing VII (2005), which employ optical elements to perform transform coding of multispectral images. Two notable previous DMD-driven applications involve confocal microscopy (Lane, P. M., Elliott, R. P., MacAulay, C. E., “Confocal microendoscopy with chromatic sectioning,” Proc. SPIE. Volume 4959 (2003) 23-26) and micro-optoelectromechanical (MOEM) systems (DeVerse, R. A., Coifman, R. R., Coppi, A. C., Fateley, W. G., Geshwind, F., Hammaker, R. M., Valenti, S., Warner, F. J., “Application of spatial light modulators for new modalities in spectrometry and imaging,” Proc. SPIE. Volume 4959 (2003)). The beauty of compressive sensing is that either Gaussian or Bernoulli white-noise patterns serve as appropriate basis functions allowing them to be disassembled into sets of two or more transmissive or reflective modulators where even intermediary combinations would still serve as mathematically acceptable patterns for encoding the image signal.